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Multi-phase System Supplied by SVM VSI: A New Fast Algorithm to Compute Duty Cycles Xavier Kestelyn, Eric Semail, J.P Hautier. L2EP, Laboratoire d’Electrotechnique et d’ Electronique de Puissance de Lille ENSAM Lille 8 bd Louis XIV F-59046 LILLE, France e-mail: [email protected] http://www.univ-lille1.fr/l2ep/

Keywords: Multi-phase, Space Vector Modulation, Fast Algorithm I. Summary Multi-phase drives are more and more often used in industry, especially for high-power applications [17] [18] [20]. Space Vector Modulation (SVM) is now widely implemented and possesses many advantages over carrier-based pulse width modulation (PWM): • Natural overmodulation implementation • Easy solution for saturation treatment • Fast and convenient to compute • Easy implementation of switching constraints for example to reduce harmonic currents [19]. Many authors proposed SVM VSI applied to multi-phase drives. For example, [2] and [15] have chosen instantaneous vectors to control dual 3-phase induction machines with low generated harmonic currents, [4] and [6] to control 5-phase machines. The initial space is split onto orthogonal subspaces (d-q and zero-sequence) and the initial reference vector can be expressed at any sampling time in terms of several reference vectors, each one belonging to one subspace (plane and/or line). Each reference vector is located onto a sector, bounded by two active vectors, and decomposed onto these vectors. Once the two vector components are known, duty ratios are determined. Then, zero vectors are chosen and switching sequencing is imposed. Due to the high number of phases, a high number of sectors exist and the location of the different reference vectors leads to a great computational requirement (Fig. 1a). Using the equivalence between a multi-phase machine and a set of fictitious one-phase or twophase machines which are magnetically independent but mechanically and electrically coupled [1][13], we propose a new fast algorithm to compute the duty cycles of each VSI leg. This algorithm, based on a vectorial approach of inverters developed in [3][7][5], thereby reduces computation time and allows to use low computational requirements. This paper shows that, compared to classical technics [11] [10] [9] [12], it is no more necessary to find the location of the reference vectors to get explicitly the duty cycle of each leg. Figure 1 shows the difference between classical algorithm (Fig. 1a) and proposed one (Fig. 1b). This proposed technique is at first illustrated on a 3-phase drive. Geometrical representations allow then to establish links with usual 3-phase SVM. The implementation of the proposed SVM is achieved in the vector control of a 5-phase drive. Experimental results are presented and confirm the theoretical approach.

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[17] [18] [19] [20] [21]

X. Kestelyn, E. Semail, J.P Hautier, Vectorial Multi-machine Modeling for a 5-Phase Machine, ICEM Brugges, August 2002, CD-ROM. Z.Yifan , T. A. Lipo, Space Vector PWM Control of Dual Three-Phase Induction Maching Using Vector Space Decomposition, IEEE Transactions on Industry Applications, Vol. 31. no 5, September/October 1995, pp. 1100-1109. E. Semail, Tools and studying method of polyphase electrical systems, Generalization of the space vector theory, Ph.D. thesis USTL(University of Sciences and Technologies of Lille), June 2000 (text in French). H.A. Toliyat, S. Ruhe, X. Huangsheng, A DSP-Based Vector Control of 5-Phase Synchronous Reluctance Motor, IEEE-IAS annual meeting 2000, Rome, october 2000, CD-ROM. E. Semail, C. Rombaut New tools for studying voltage-source inverters, IEEE Power Engineering Review, Vol. 22. no 3, March 2002, pp. 47-48 J. P. Martin , E. Semail , S. Pierfederici,A. Bouscayrol, F. Meibody-Tabar , B. Davat, Space Vector Control of 5-phase PMSM supplied by q H-bridge VSIs, ElectrIMACS 2002, Montreal, August 2002, CDROM. E. Semail , C. Rombaut, New method to calculate the conduction durations of the switches in a n-leg 2-level Voltage Source, EPE 2001, 27-29 August, 2001, Graz, Austria,CDROM. D. Gondouin, F. Menneron New diesel-electric propulsion system topologies, AES2000, October 2000, Paris, pp. 66-71. A. Hava, R. Kerkman ,T. Lipo, Carrier-basisd PWM VSI overmodulation strategies: analysis, comparison and design, IEEE Trans. on Power Electronics, vol. 13, no. 4, July 1998, pp. 624-689. W. Leonhard., 30 years space vectors, 20 years field orientation, 10 years digital signal processing with controlled AC drives, EPE Journal, vol. 1, no. 1, July 1991, pp. 13-20. J. Holtz, Pulse width modulation - A survey, IEEE Trans. on Industrial Electronics, vol. 39 no. 5, December 1992, pp. 410-419. V. Blasko Analysis of a hybrid PWM basisd on modified space vector and triangle-comparison methods, IEEE Transactions on industry applications, Vol. 33, No. 1, May/June 1997,pp. 756-764. E. Semail, A. Bouscayrol,J.P. Hautier, Vectorial formalism for analysis and design of polyphase synchronous machines, EPJ Applied Physics, EPJ AP (European Physical Journal-Applied Physics), Vol. 22, no. 3, June 2003, pp. 207-220. P. Delarue,A. Bouscayrol ,E. Semail Generic Control Method of Multileg Voltage-Source-Converters for Fast Practical Implementation, IEEE Trans. on Power Electronics, vol. 18, no. 2, March 2003, pp. 517-526. D. Hadiouche,H. Razik,A. Rezzoug Modelling of a Double Star Induction Motor for Space Vector PWM Control, ICEM 2000, August 2000, Espoo (Finland), pp. 392-396. A. Bouscayrol, B. Davat, B. de Fornel, B. Fran¸cois, J. P. Hautier, F. Meibody-Tabar, M. PietrzakDavid. Multi-machine Multi-converter System: application for the electromechanical drives, EPJ Applied Physics, Vol. 10, no. 2, May 2000, pp-131-147, (common paper of GREEN, L2EP and LEEI, according to the MMS project of the French GdR-SDSE). Bhatia R., Krattiger H., Bonanini A., Schafer D., Inge J.T., Sydnor G.H. Adjustable Speed Drive With A Single 100-MW Synchronous Motor ABB Review Issue, No6, 1998, pp.14-20. H. Godfroi, P. Bosc. Large variable speed drives using synchronous motors and frequency converters Alstom Review nˇr6, 1986. S. Siala S., E. Guette, J. L. Pouliquen. Multi-inverter PWM control: a new generation drives for cruise ship electric propulsion, European Power Electronics Conference (EPE2003), Toulouse (France), CDROM. D. Beliaev, A. Weinger, B. Ingram, F. DeWinter. Polyphase Systems For High-Power Controlled AC, European Power Electronics Conference (EPE2003), Toulouse (France), CD-ROM. T.M Jahns. Improved reliability in solid-state ac drives by means of multiple independent phase-drive units, IEEE Transactions on Industry Applications, Vol. IA16, pp 321-331, May/June 1980.

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Xavier Kestelyn was born in France in 1971. He received the teaching degree ”Agr´egation” in 1997 and Ph.D. degree in electrical engineering in 2003 in University of Sciences and Technology of Lille (France). He is a member of the Multi-Machine Multi-Converter System national French project of research. His fields of interest include Modelling, Control and Design of Polyphase Systems (Converters and AC Drives).

Eric Semail is graduated from the Ecole Normale Sup´erieure, Cachan, France. He received the teaching degree ”Agr´egation” in 1986. From 1987 to 2001, he has been professor (holder of agr´egation) in University of Lille (USTL). He received Ph.D. degree in 2000 and became associate professor at ENSAM Lille in 2001. In L2EP (Laboratory of Electrical Engineering of Lille) his fields of interest include modeling, control and design of polyphase systems (converters and AC Drives)

Jean-Paul Hautier received the Ph.D. degree from the University of Lille (USTL), France, in 1984. He received the ”Habilitation ` a diriger des Recherches” degree from Engineering School of Douai, France, in 1989. In 1989, he became Professor at the ENSAM Lille. Its main research interests are power electronics and electrical systems control. Since 2000, Pr. Hautier has the head of the the L2EP Lille (Laboratory of Electrical Engineering of Lille).